Over-excitation protection is used to protect generators and power transformers against excessive flux density and saturation of magnetic core. The function calculates U/f ratio (Volts/Hertz) proportional to excitation level of generator or transformer and compares this value to the setting limit. The function starts when the excitation level exceeds a set limit and operates when a set operating time has then elapsed. The operating time characteristic can be selected to be either definite time (DT) or over-excitation inverse definite minimum time (over-excitation type IDMT).
Protection relay manufacturers have modeled the over-excitation IDMT characteristics by using several base equations. One of the presented base equations for the IDMT curve is as follows:
                              t          ⁡                      (            s            )                          =                  60          *                      ⅇ                          (                                                ak                  +                  b                  -                                      100                    ⁢                                                                                  ⁢                    M                                                  c                            )                                                          (        1        )            
t(s) the operating time in seconds
M the excitation level (‘U/f ratio’ or ‘Volts/Hertz’) in per unit (p.u.) value
k time multiplier
Inherently this thermal model equation gives result as minutes. The constant ‘60’ in Equation 1 converts the time from minutes to seconds. The curve parameters a, b and c can be constants defined by the vendor. The vendor may provide several curves, which have mutually different constant values a, b and c or these parameters can be settable by the user. As an example, a may be 2.50, b may be 115.00 and c may be 4.886. Generally, Equation 1 represents a known thermal model mathematically defined by a base equation, where the base value is the natural base e≈2.7182818285. These kinds of equations where the base number exceeds unity, inherently grow very rapidly due to the increasing exponent.
Operating time can be calculated directly from equation by integration, where cumulated integral values comprises (e.g., consists of) successive 1/t-values calculated from Equation 1 inverses. This widely used method is inherently prone to accuracy problems during integration due to high denominator values resulting to integral sum components close to zero.
If we can assume parameters a, b and c to be vendor defined, and by this way manageable (i.e., we can guarantee curve characteristics depending on these parameters already before hand), the problematic parameters in Equation 1 are the user-settable parameter k and equation variable M. Frequently, the value of the user-settable k value has been limited severely. For instance, some vendors allow only k values that are between 1 and 9.
In the known calculation method, the successive 1/t values are beforehand calculated to look-up-table (LUT) and are integrated to an integral sum. If the values are close to zero, calculation inaccuracy problems are caused when there is some variation in input signal magnitude (here M) level, because an integral component almost zero will be incremented to a remarkably larger cumulated integral sum. Another drawback in the known method, if no beforehand calculated LUT is used, is the need of a long division calculation operation in every task cycle. Both these two drawbacks (successive execution period divisions and cumulation inaccuracy) can be replaced by a multiplication and comparison method disclosed in WO 2009/080865.
However, in some application environments, it would be preferable to allow greater values for k, up to 100 or even more. With high k values together with low or modest M values the base equation value increases rapidly. Consequently, this leads to substantially long protection operating times.
More problems may also arise if the parameters a, b and c are user-settable in Equation 1. While technology and customer needs are progressing in the future there will surely be more demands regarding parameter flexibility. The parameter value combination may be such that the calculation of the equation becomes computationally highly time consuming.
Parameter value ranges should be successfully restricted by a vendor so that equation can reach only manageable and pre-estimated values. It has to be guaranteed that all possible parameter combinations lead to a correctly calculated operating time, i.e. base equation result can never grow beyond computational limits so that no processor overflow occurs.